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Assignments week 4 Computational neuroscience
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Before you turn this problem in, make sure everything runs as expected. First, restart thekernel (in the menubar, select Kernel→Restart) and then run all cells (in the menubar,
select Cell→Run All).
Make sure you fill in any place that says YOUR CODE HERE or "YOUR ANSWER HERE", as
well as your name and collaborators below:
NAME = Kiki Boumans
COLLABORATORS =
File "<ipython-input-1-342a7c538cbf>", line 1
NAME = Kiki Boumans
^
SyntaxError: invalid syntax
Assignments week 4
Complete the assignments below, save the notebook and submit them on canvas.
Assignment 4.1
According to the Hodgkin classification does the Hodgkin-Huxley neuron exhibit class 1
excitability or class 2 excitability? Justify your choice.
Class 1 excitability: Action potentials can be generated with arbitrarily low frequency,
depending on the strength of the input current. The F-I curve is continuous. Class 2
excitability: Action potentials can be only be generated within a limited frequency band.
The F-I curve is discontinuous.
Hodgkin-Huxley neurons exhibit class 2 excitability, because strengthening the input
current will increase the firing rate of the neuron. If the input current would be used as a
bifurcation parameter (parameter that changes the stability of the equilibrium, in this case
the action potential) then the Hodgkin-Huxley model undergoes a socalled Hopf
bifurcation. However, due to the Hopf bifurcation there is a minimum firing rate for the
neurons. This indicates that either the neuron is not firing at all, or firing at the minimum
firing rate, which is also called the all-or-none principle. Due to this principle, there is no
continuous increase in action potential amplitude, but it is discontinuous with sudden
jumps in amplitude.
Assignment 4.2
Find the fixed-points of the 1-dimensional dynamical system defined by $ \dot x = rx - x^3
$ and determine whether they are attractors or repellors for r =0.5.
$ \dot x = rx - x^3 $
The fixed points are ẋ=0 and x=0
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